This might not be the best solution, but we can use the multiple choice nature to our advantage.

n = 1 is easily verified true, which rules out A and C. In order to test between B and D, all we need is to check n = 5.

We want to know what is modulo 2^5. So, reduce to which turns out to be congruent to 16 mod 32. (On paper we can do 7 * 49 * 49 + 9 * 81 * 81 which becomes 7 * 17 * 17 + 9 * 17 * 17 which is just 16 * 17 * 17 which is clearly divisible by 16 but not 32.) So the answer is D.